EXST7015 Fall2011 Appendix 08

EXST7015 Fall2011 Appendix 08 - Statistical Techniques II...

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Unformatted text preview: Statistical Techniques II Large example and Variable selection Appendix 8 Annotated SAS example Page 186 1 dm'log;clear;output;clear'; 2 OPTIONS PS=512 LS=101 NOCENTER NODATE NONUMBER FORMCHAR="|----|+|---+=|-/\<>*"; 3 4 TITLE1 'Appendix08: Hospital infection rate study'; 5 TITLE2 'SENIC database from NKNW 1996 (Appendix C)'; 6 7 filename input 'Appendix08 MReg-SENIC.DAT'; 8 ODS HTML style=minimal body='Appendix08 MReg-SENIC.html' ; NOTE: Writing HTML Body file: Appendix08 MReg-SENIC.html 9 %let DepVarList = LtofStay Age CulRatio XRay NoBeds Census Nurses Services; 10 11 ***********************************************************************; 12 *** SENIC hospital study from Appendix C of: ***; 13 *** Neter, J., Kutner, M. H., Nachtsheim, C. J., and Wasserman, W., ***; 14 *** Applied Linear Statistical Models, 4th Edition, Richard D. ***; 15 *** Irwin, Inc., Burr Ridge, Illinois, 1996. ***; 16 ***********************************************************************; 17 18 DATA SENIC; Infile input missover; 19 INPUT IDNo LtofStay Age InfRisk CulRatio XRay NoBeds MedSch 20 Region Census Nurses Services; 21 *** label IDNo = 'Identification number' 22 LtofStay = 'Length of stay (days)' 23 Age = 'Patient age (years)' 24 InfRisk = 'Average Infection risk (%)' 25 CulRatio = 'ratio cultures to patients w/o symptoms' 26 XRay = 'ratio xrays to patients w/o symptoms' 27 NoBeds = 'Average no. of beds in hosp.' 28 MedSch = 'Med School Affiliation' 29 Region = 'Region NE, NC, S, W' 30 Census = 'Average no. patients in hosp.' 31 Nurses = 'Av. no. nurses' 32 Services = '% of 35 potential service facilities'; 33 CARDS; Run; NOTE: 113 records were read from the infile INPUT. The minimum record length was 61. The maximum record length was 61. NOTE: The data set WORK.SENIC has 113 observations and 12 variables. NOTE: DATA statement used (Total process time): real time 0.01 seconds cpu time 0.01 seconds 33 34 ; 35 Proc print data=SENIC; RUN; NOTE: There were 113 observations read from the data set WORK.SENIC. NOTE: The PROCEDURE PRINT printed page 1. NOTE: PROCEDURE PRINT used (Total process time): real time 0.18 seconds cpu time 0.07 seconds SENIC database from NKNW 1996 (Appendix C) Ltof Inf Cul Obs IDNo Stay Age Risk Ratio 1 2 3 4 5 6 7 8 9 10 . . . 111 112 113 XRay No Beds Med Sch Region Census Nurses Services 1 2 3 4 5 6 7 8 9 10 7.13 8.82 8.34 8.95 11.20 9.76 9.68 11.18 8.67 8.84 55.7 58.2 56.9 53.7 56.5 50.9 57.8 45.7 48.2 56.3 4.1 1.6 2.7 5.6 5.7 5.1 4.6 5.4 4.3 6.3 9.0 3.8 8.1 18.9 34.5 21.9 16.7 60.5 24.4 29.6 39.6 51.7 74.0 122.8 88.9 97.0 79.0 85.8 90.8 82.6 279 80 107 147 180 150 186 640 182 85 2 2 2 2 2 2 2 1 2 2 4 2 3 4 1 2 3 2 3 1 207 51 82 53 134 147 151 399 130 59 241 52 54 148 151 106 129 360 118 66 60.0 40.0 20.0 40.0 40.0 40.0 40.0 60.0 40.0 40.0 111 112 113 7.70 17.94 9.41 56.9 56.2 59.5 4.4 5.9 3.1 12.2 26.4 20.6 67.9 91.8 91.7 129 835 29 2 1 2 4 1 3 85 791 20 136 407 22 62.9 62.9 22.9 James P. Geaghan - Copyright 2011 Statistical Techniques II Large example and Variable selection 140 141 142 144 145 146 147 NOTE: NOTE: 148 NOTE: NOTE: NOTE: Appendix 8 Annotated SAS example Page 187 proc reg data=SENIC all LINEPRINTER; TITLE2 'Full Model with diagnostics'; model InfRisk = &DepVarList / all influence collin partial; output out=next1 p=YHat r=e; OPTIONS PS=50 LS=160; PLOT RESIDUAL.*PREDICTED. / VREF=0; OPTIONS PS=60 LS=120; Run; 113 observations read. 113 observations used in computations. OPTIONS PS=50 LS=130; The data set WORK.NEXT1 has 113 observations and 14 variables. The PROCEDURE REG printed pages 2-28. PROCEDURE REG used: real time 0.63 seconds cpu time 0.22 seconds proc plot data=next1; PLOT e*YHat / VREF=0; run; OPTIONS PS=256 LS=121; 149 150 151 152 NOTE: There were 113 observations read from the data set WORK.NEXT1. NOTE: The PROCEDURE PLOT printed page 29. NOTE: PROCEDURE PLOT used: real time 0.02 seconds cpu time 0.01 seconds SENIC database from NKNW 1996 (Appendix C) Full Model with diagnostics The REG Procedure Descriptive Statistics Uncorrected Variable Sum Mean SS Intercept 113.00000 1.00000 113.00000 LtofStay 1090.26000 9.64832 10928 Age 6015.20000 53.23186 322430 CulRatio 1784.60000 15.79292 39916 XRay 9224.00000 81.62832 794935 NoBeds 28495 252.16814 11350621 Census 21625 191.37168 6786317 Nurses 19577 173.24779 5563895 Services 4877.00000 43.15929 236367 InfRisk 492.10000 4.35487 2344.41000 Variance 0 3.65366 19.90594 104.74924 374.95776 37188 23642 19395 231.06619 1.79803 Standard Deviation 0 1.91146 4.46161 10.23471 19.36383 192.84269 153.75956 139.26539 15.20086 1.34091 Variable Intercept LtofStay Age CulRatio XRay NoBeds Census Nurses Services InfRisk Uncorrected Sums of Squares and Crossproducts Intercept LtofStay Age CulRatio 113 1090.26 6015.2 1784.6 1090.26 10928.3862 58217.008 17934.179 6015.2 58217.008 322429.74 93842.53 1784.6 17934.179 93842.53 39915.96 9224 90581.657 490828.22 155106.57 28495 291825.09 1511173.4 480905.9 21625 224243.93 1146930.4 366716.9 19577 199032.96 1036347.9 340930 4877 48211.858 259304.51 80247.9 492.1 4901.071 26196.13 8631.16 XRay 9224 90581.657 490828.22 155106.57 794934.88 2345162.1 1786191.9 1621409.2 401791.21 41487.8 Variable Intercept LtofStay Age CulRatio XRay NoBeds Census Nurses Services InfRisk Uncorrected Sums of Squares and Crossproducts NoBeds Census Nurses Services 28495 21625 19577 4877 291825.09 224243.93 199032.96 48211.858 1511173.4 1146930.4 1036347.9 259304.51 480905.9 366716.9 340930 80247.9 2345162.1 1786191.9 1621409.2 401791.21 11350621 8710988 7690447 1490677.5 8710988 6786317 5923892 1136997.3 7690447 5923892 5563895 1030697.7 1490677.5 1136997.3 1030697.7 236367.28 134511.4 102981.5 93495.4 22180.61 InfRisk 492.1 4901.071 26196.13 8631.16 41487.8 134511.4 102981.5 93495.4 22180.61 2344.41 James P. Geaghan - Copyright 2011 Statistical Techniques II Large example and Variable selection Appendix 8 Annotated SAS example Page 188 SENIC database from NKNW 1996 (Appendix C) Full Model with diagnostics The REG Procedure Variable LtofStay Age CulRatio XRay NoBeds Census Nurses Services InfRisk Variable LtofStay Age CulRatio XRay NoBeds Census Nurses Services InfRisk Correlation Age CulRatio 0.1889 0.3267 1.0000 -0.2258 -0.2258 1.0000 -0.0189 0.4250 -0.0588 0.1397 -0.0548 0.1429 -0.0829 0.1989 -0.0405 0.1851 0.0011 0.5592 LtofStay 1.0000 0.1889 0.3267 0.3825 0.4093 0.4739 0.3404 0.3555 0.5334 Census 0.4739 -0.0548 0.1429 0.0629 0.9810 1.0000 0.9079 0.7781 0.3814 Correlation Nurses 0.3404 -0.0829 0.1989 0.0774 0.9155 0.9079 1.0000 0.7835 0.3940 XRay 0.3825 -0.0189 0.4250 1.0000 0.0458 0.0629 0.0774 0.1119 0.4534 Services 0.3555 -0.0405 0.1851 0.1119 0.7945 0.7781 0.7835 1.0000 0.4126 NoBeds 0.4093 -0.0588 0.1397 0.0458 1.0000 0.9810 0.9155 0.7945 0.3598 InfRisk 0.5334 0.0011 0.5592 0.4534 0.3598 0.3814 0.3940 0.4126 1.0000 Variable Intercept LtofStay Age CulRatio XRay NoBeds Census Nurses Services InfRisk Intercept 113 1090.26 6015.2 1784.6 9224 28495 21625 19577 4877 492.1 Model Crossproducts LtofStay 1090.26 10928.3862 58217.008 17934.179 90581.657 291825.09 224243.93 199032.96 48211.858 4901.071 X'X X'Y Y'Y Age 6015.2 58217.008 322429.74 93842.53 490828.22 1511173.4 1146930.4 1036347.9 259304.51 26196.13 CulRatio 1784.6 17934.179 93842.53 39915.96 155106.57 480905.9 366716.9 340930 80247.9 8631.16 XRay 9224 90581.657 490828.22 155106.57 794934.88 2345162.1 1786191.9 1621409.2 401791.21 41487.8 Variable Intercept LtofStay Age CulRatio XRay NoBeds Census Nurses Services InfRisk NoBeds 28495 291825.09 1511173.4 480905.9 2345162.1 11350621 8710988 7690447 1490677.5 134511.4 Model Crossproducts Census 21625 224243.93 1146930.4 366716.9 1786191.9 8710988 6786317 5923892 1136997.3 102981.5 X'X X'Y Y'Y Nurses 19577 199032.96 1036347.9 340930 1621409.2 7690447 5923892 5563895 1030697.7 93495.4 Services 4877 48211.858 259304.51 80247.9 401791.21 1490677.5 1136997.3 1030697.7 236367.28 22180.61 InfRisk 492.1 4901.071 26196.13 8631.16 41487.8 134511.4 102981.5 93495.4 22180.61 2344.41 Variable Intercept LtofStay Age CulRatio XRay NoBeds Census Nurses Services InfRisk Intercept 1.5858508096 -0.001322824 -0.025196942 -0.002266262 -0.001378744 -0.000134192 0.000244251 9.3582332E-6 -0.002065552 -0.747255248 X'X Inverse, Parameter Estimates, and SSE LtofStay Age CulRatio -0.001322824 -0.025196942 -0.002266262 0.0051859266 -0.000559317 -0.000236511 -0.000559317 0.0005385865 0.0000791345 -0.000236511 0.0000791345 0.0001256418 -0.000125206 3.7315905E-6 -0.000018668 0.0000554848 -5.086015E-6 -1.744267E-6 -0.000120582 0.0000114987 6.2102827E-6 0.0000327339 -1.741494E-6 -3.965013E-6 -0.00003638 -5.727461E-6 -4.319302E-6 0.1769313961 0.016213596 0.0469933765 XRay -0.001378744 -0.000125206 3.7315905E-6 -0.000018668 0.0000327219 1.2384372E-7 1.3610934E-6 -6.872235E-7 -3.724035E-6 0.0120368799 Variable Intercept LtofStay Age CulRatio XRay NoBeds Census Nurses Services InfRisk NoBeds -0.000134192 0.0000554848 -5.086015E-6 -1.744267E-6 1.2384372E-7 7.9876579E-6 -8.96859E-6 -8.686793E-7 -6.032734E-6 -0.00144718 X'X Inverse, Parameter Estimates, and SSE Census Nurses Services 0.000244251 9.3582332E-6 -0.002065552 -0.000120582 0.0000327339 -0.00003638 0.0000114987 -1.741494E-6 -5.727461E-6 6.2102827E-6 -3.965013E-6 -4.319302E-6 1.3610934E-6 -6.872235E-7 -3.724035E-6 -8.96859E-6 -8.686793E-7 -6.032734E-6 0.0000131054 -1.498917E-6 2.5756281E-6 -1.498917E-6 3.3422233E-6 -4.330367E-6 2.5756281E-6 -4.330367E-6 0.0001128895 0.0007279559 0.001906211 0.0162795745 InfRisk -0.747255248 0.1769313961 0.016213596 0.0469933765 0.0120368799 -0.00144718 0.0007279559 0.001906211 0.0162795745 95.639819869 James P. Geaghan - Copyright 2011 Statistical Techniques II Large example and Variable selection Appendix 8 Annotated SAS example Page 189 SENIC database from NKNW 1996 (Appendix C) Full Model with diagnostics The REG Procedure Model: MODEL1 Dependent Variable: InfRisk Analysis of Variance Source Model Error Corrected Total Root MSE Dependent Mean Coeff Var Sum of Squares 105.74000 95.63982 201.37982 DF 8 104 112 0.95896 4.35487 22.02053 R-Square Adj R-Sq Mean Square 13.21750 0.91961 F Value 14.37 Pr > F <.0001 0.5251 0.4885 Parameter Estimates Variable Intercept LtofStay Age CulRatio XRay NoBeds Census Nurses Services Variable Intercept LtofStay Age CulRatio XRay NoBeds Census Nurses Services DF 1 1 1 1 1 1 1 1 1 Parameter Estimate -0.74726 0.17693 0.01621 0.04699 0.01204 -0.00145 0.00072796 0.00191 0.01628 Standard Error 1.20763 0.06906 0.02226 0.01075 0.00549 0.00271 0.00347 0.00175 0.01019 DF 1 1 1 1 1 1 1 1 1 Squared Partial Corr Type I . 0.28456 0.01440 0.22153 0.03481 0.06108 0.00174 0.02016 0.02396 Squared Semi-partial Corr Type II . 0.02998 0.00242 0.08728 0.02199 0.00130 0.00020079 0.00540 0.01166 t Value -0.62 2.56 0.73 4.37 2.19 -0.53 0.21 1.09 1.60 Pr > |t| 0.5374 0.0118 0.4679 <.0001 0.0304 0.5945 0.8343 0.2794 0.1131 Type I SS 2143.03018 57.30511 2.07506 31.45735 3.84765 6.51642 0.17436 2.01642 2.34765 Parameter Estimates Squared Partial Corr Type II Tolerance . . 0.05937 0.47122 0.00508 0.83281 0.15525 0.67842 0.04425 0.72772 0.00273 0.03006 0.00042261 0.02882 0.01124 0.13774 0.02396 0.34229 Type II SS 0.35211 6.03648 0.48809 17.57678 4.42782 0.26220 0.04044 1.08719 2.34765 Variance Inflation 0 2.12214 1.20076 1.47402 1.37416 33.26931 34.70183 7.26005 2.92151 Standardized Estimate 0 0.25221 0.05395 0.35868 0.17382 -0.20813 0.08347 0.19798 0.18455 Squared Semi-partial Corr Type I . 0.28456 0.01030 0.15621 0.01911 0.03236 0.00086581 0.01001 0.01166 95% Confidence Limits -3.14203 1.64752 0.03999 0.31388 -0.02792 0.06035 0.02568 0.06831 0.00116 0.02291 -0.00682 0.00393 -0.00616 0.00761 -0.00157 0.00538 -0.00393 0.03648 Variable Intercept LtofStay Age CulRatio XRay NoBeds Census Nurses Services Intercept 1.4583700555 -0.001216487 -0.023171451 -0.002084085 -0.001267912 -0.000123405 0.0002246165 8.6059591E-6 -0.00189951 Covariance of Estimates LtofStay Age -0.001216487 -0.023171451 0.0047690489 -0.000514356 -0.000514356 0.0004952915 -0.000217498 0.0000727731 -0.000115141 3.4316216E-6 0.0000510246 -4.677169E-6 -0.000110889 0.0000105743 0.0000301025 -1.601502E-6 -0.000033456 -5.267051E-6 CulRatio -0.002084085 -0.000217498 0.0000727731 0.0001155419 -0.000017167 -1.604051E-6 5.7110607E-6 -3.64628E-6 -3.972089E-6 Variable Intercept LtofStay Age CulRatio XRay NoBeds Census Nurses Services NoBeds -0.000123405 0.0000510246 -4.677169E-6 -1.604051E-6 1.1388838E-7 7.3455592E-6 -8.247638E-6 -7.988493E-7 -5.547785E-6 Covariance of Estimates Census Nurses 0.0002246165 8.6059591E-6 -0.000110889 0.0000301025 0.0000105743 -1.601502E-6 5.7110607E-6 -3.64628E-6 1.2516801E-6 -6.319801E-7 -8.247638E-6 -7.988493E-7 0.0000120519 -1.378425E-6 -1.378425E-6 3.0735542E-6 2.3685827E-6 -3.982265E-6 Services -0.00189951 -0.000033456 -5.267051E-6 -3.972089E-6 -3.424674E-6 -5.547785E-6 2.3685827E-6 -3.982265E-6 0.0001038147 XRay -0.001267912 -0.000115141 3.4316216E-6 -0.000017167 0.0000300915 1.1388838E-7 1.2516801E-6 -6.319801E-7 -3.424674E-6 James P. Geaghan - Copyright 2011 Statistical Techniques II Large example and Variable selection Appendix 8 Annotated SAS example Page 190 SENIC database from NKNW 1996 (Appendix C) Full Model with diagnostics The REG Procedure Model: MODEL1 Dependent Variable: InfRisk Variable Intercept LtofStay Age CulRatio XRay NoBeds Census Nurses Services Variable Intercept LtofStay Age CulRatio XRay NoBeds Census Nurses Services NoBeds -0.0377 0.2726 -0.0775 -0.0551 0.0077 1.0000 -0.8766 -0.1681 -0.2009 Correlation of Estimates LtofStay Age -0.0146 -0.8622 1.0000 -0.3347 -0.3347 1.0000 -0.2930 0.3042 -0.3039 0.0281 0.2726 -0.0775 -0.4625 0.1369 0.2486 -0.0410 -0.0475 -0.0232 Intercept 1.0000 -0.0146 -0.8622 -0.1606 -0.1914 -0.0377 0.0536 0.0041 -0.1544 Correlation of Estimates Census 0.0536 -0.4625 0.1369 0.1530 0.0657 -0.8766 1.0000 -0.2265 0.0670 Sequential Parameter Estimates Intercept LtofStay 4.354867 0 0.744304 0.374217 2.265909 0.387916 0.397766 0.269740 -0.083236 0.239464 -0.424573 0.169755 -0.393711 0.157208 -0.449386 0.182178 -0.747255 0.176931 NoBeds 0 0 0 0 0 0.001403 0.000299 -0.000577 -0.001447 Number 1 2 3 4 5 6 7 8 9 Eigenvalue 7.92221 0.70667 0.23449 0.04727 0.03554 0.02878 0.01657 0.00546 0.00301 Number 1 2 3 4 5 6 7 8 9 Census 0.00014895 0.00351 8.741457E-8 0.05162 0.00000597 0.00018174 0.00117 0.93113 0.01224 Nurses 0.0041 0.2486 -0.0410 -0.1935 -0.0657 -0.1681 -0.2265 1.0000 -0.2229 CulRatio -0.1606 -0.2930 0.3042 1.0000 -0.2911 -0.0551 0.1530 -0.1935 -0.0363 XRay -0.1914 -0.3039 0.0281 -0.2911 1.0000 0.0077 0.0657 -0.0657 -0.0613 Services -0.1544 -0.0475 -0.0232 -0.0363 -0.0613 -0.2009 0.0670 -0.2229 1.0000 Age 0 0 -0.031067 0.008351 0.008050 0.017327 0.018602 0.017040 0.016214 CulRatio 0 0 0 0.057623 0.050572 0.050376 0.050908 0.047616 0.046993 Sequential Parameter Estimates Census Nurses 0 0 0 0 0 0 0 0 0 0 0 0 0.001472 0 0.000357 0.002531 0.000728 0.001906 Services 0 0 0 0 0 0 0 0 0.016280 Condition Index 1.00000 3.34824 5.81248 12.94588 14.93049 16.59008 21.86586 38.09407 51.29072 XRay 0 0 0 0 0.011031 0.013107 0.013235 0.012574 0.012037 Collinearity Diagnostics -----------------------------Proportion of Variation----------------------------Intercept LtofStay Age CulRatio XRay NoBeds 0.00008203 0.00026608 0.00008384 0.00241 0.00055647 0.00014889 0.00062369 0.00113 0.00066774 0.02105 0.00504 0.00316 0.00150 0.00158 0.00222 0.67694 0.00076682 0.00000481 0.00082735 0.04556 0.00039099 0.00635 0.00030739 0.02079 0.00123 0.00104 0.00130 0.09639 0.43090 0.00276 0.01898 0.01720 0.02926 0.06172 0.48518 0.00092814 0.03592 0.60385 0.02075 0.05279 0.05646 0.10941 0.03300 0.27836 0.00195 0.01730 0.00245 0.85653 0.90784 0.05102 0.94338 0.06505 0.01834 0.00627 Nurses 0.00070822 0.01543 0.00219 0.47665 0.22472 0.13803 0.13349 0.00712 0.00166 Services 0.00057691 0.00004055 0.00244 0.11157 0.43144 0.36303 0.06932 0.01485 0.00673 James P. Geaghan - Copyright 2011 Statistical Techniques II Large example and Variable selection Appendix 8 Annotated SAS example Page 191 SENIC database from NKNW 1996 (Appendix C) Full Model with diagnostics The REG Procedure Model: MODEL1 Dependent Variable: InfRisk Output Statistics Obs 1 2 3 4 5 6 7 8 9 10 11 12 13 14 15 16 17 18 19 20 21 22 23 24 25 26 27 28 29 30 31 32 33 34 35 36 37 38 39 40 41 42 43 44 45 46 47 48 49 50 51 52 53 54 55 56 57 58 59 60 61 62 63 64 65 66 67 68 69 70 71 72 73 74 Dep Var Predicted Std Error InfRisk Value Mean Predict 4.1000 3.5001 0.3025 1.6000 3.2294 0.2303 2.7000 3.2557 0.2019 5.6000 4.8324 0.3086 5.7000 5.6179 0.2338 5.1000 4.7448 0.1833 4.6000 4.3761 0.1467 5.4000 6.8749 0.5686 4.3000 4.5152 0.1671 6.3000 4.8118 0.2339 4.9000 6.7534 0.3947 4.3000 3.5753 0.1927 7.7000 7.3160 0.3647 3.7000 4.2070 0.2082 4.2000 3.6547 0.2068 5.5000 5.0455 0.3143 4.5000 4.5928 0.2155 6.4000 5.2613 0.1774 4.2000 3.6730 0.1499 4.1000 4.9375 0.4201 4.2000 3.8105 0.3312 4.8000 5.6847 0.2423 5.0000 4.9035 0.2109 4.8000 4.9061 0.3527 4.0000 4.5309 0.1766 3.9000 4.7168 0.3373 4.5000 5.0818 0.2135 3.2000 3.3972 0.1926 4.4000 4.9918 0.1704 4.9000 4.5468 0.1700 5.0000 5.4726 0.2575 5.2000 4.7400 0.2468 5.3000 4.4081 0.2659 6.1000 5.9570 0.2454 6.3000 4.3256 0.1711 5.0000 5.1517 0.2032 2.8000 4.2150 0.1698 4.6000 3.4214 0.2044 4.1000 4.0817 0.2365 1.3000 2.6742 0.2781 3.7000 3.9159 0.1748 4.7000 4.9090 0.1576 3.0000 3.7888 0.3245 5.6000 4.6250 0.1662 5.5000 3.9156 0.1419 4.6000 4.5727 0.4242 6.5000 6.7821 0.5490 5.5000 4.1778 0.3715 1.8000 2.2184 0.3082 4.2000 4.1237 0.1562 5.6000 5.2600 0.2160 4.3000 4.1467 0.3460 7.6000 5.0438 0.3878 7.8000 6.3393 0.4085 3.1000 3.2399 0.1803 3.9000 4.3604 0.1821 3.7000 3.0107 0.2188 4.3000 4.0995 0.2552 3.9000 5.2170 0.2057 4.5000 4.7098 0.1862 3.4000 3.6326 0.2324 5.7000 5.0145 0.3804 5.4000 3.7195 0.3105 4.4000 4.0297 0.1988 5.0000 4.2063 0.2820 4.3000 5.0302 0.4047 4.4000 4.2694 0.2055 3.7000 4.1120 0.2099 4.5000 3.9764 0.3032 3.5000 4.2224 0.1981 4.2000 3.6541 0.1704 2.0000 3.0916 0.1828 5.2000 4.1729 0.1431 4.5000 5.8951 0.3613 95% CL Mean 2.9002 4.0999 2.7727 3.6862 2.8553 3.6560 4.2204 5.4444 5.1542 6.0816 4.3812 5.1083 4.0853 4.6670 5.7473 8.0026 4.1839 4.8465 4.3481 5.2756 5.9706 7.5361 3.1932 3.9575 6.5927 8.0392 3.7942 4.6198 3.2446 4.0648 4.4223 5.6687 4.1655 5.0201 4.9095 5.6131 3.3757 3.9703 4.1044 5.7706 3.1537 4.4674 5.2043 6.1651 4.4854 5.3216 4.2066 5.6056 4.1807 4.8810 4.0480 5.3856 4.6584 5.5052 3.0152 3.7792 4.6539 5.3296 4.2096 4.8840 4.9619 5.9833 4.2505 5.2295 3.8807 4.9355 5.4704 6.4435 3.9863 4.6649 4.7488 5.5546 3.8782 4.5518 3.0160 3.8268 3.6126 4.5507 2.1228 3.2256 3.5693 4.2626 4.5965 5.2214 3.1453 4.4323 4.2955 4.9546 3.6343 4.1969 3.7315 5.4139 5.6935 7.8707 3.4411 4.9145 1.6073 2.8295 3.8140 4.4333 4.8316 5.6885 3.4606 4.8328 4.2748 5.8129 5.5292 7.1495 2.8824 3.5973 3.9992 4.7215 2.5768 3.4447 3.5935 4.6055 4.8092 5.6248 4.3405 5.0791 3.1717 4.0936 4.2602 5.7688 3.1039 4.3352 3.6356 4.4238 3.6471 4.7654 4.2277 5.8327 3.8619 4.6770 3.6957 4.5283 3.3752 4.5776 3.8296 4.6152 3.3161 3.9921 2.7292 3.4540 3.8890 4.4567 5.1786 6.6115 95% CL Predict 1.5060 5.4941 1.2737 5.1852 1.3123 5.1990 2.8347 6.8301 3.6605 7.5753 2.8087 6.6809 2.4523 6.2999 4.6641 9.0858 2.5849 6.4455 2.8544 6.7692 4.6969 8.8098 1.6357 5.5150 5.2814 9.3505 2.2611 6.1530 1.7093 5.6001 3.0443 7.0467 2.6437 6.5419 3.3273 7.1952 1.7482 5.5977 2.8614 7.0136 1.7986 5.8224 3.7233 7.6461 2.9564 6.8506 2.8799 6.9323 2.5972 6.4645 2.7009 6.7326 3.1336 7.0300 1.4576 5.3369 3.0603 6.9232 2.6155 6.4781 3.5035 7.4416 2.7763 6.7036 2.4346 6.3815 3.9940 7.9199 2.3939 6.2573 3.2078 7.0956 2.2838 6.1463 1.4770 5.3658 2.1230 6.0403 0.6942 4.6542 1.9829 5.8489 2.9818 6.8362 1.7812 5.7964 2.6950 6.5550 1.9933 5.8380 2.4933 6.6521 4.5909 8.9733 2.1384 6.2171 0.2210 4.2159 2.1970 6.0504 3.3107 7.2094 2.1251 6.1683 2.9926 7.0951 4.2723 8.4064 1.3049 5.1748 2.4247 6.2960 1.0602 4.9613 2.1316 6.0673 3.2721 7.1619 2.7726 6.6470 1.6759 5.5893 2.9687 7.0603 1.7207 5.7184 2.0876 5.9718 2.2241 6.1884 2.9661 7.0942 2.3246 6.2143 2.1653 6.0587 1.9820 5.9708 2.2806 6.1642 1.7226 5.5856 1.1557 5.0275 2.2502 6.0956 3.8629 7.9272 Residual 0.5999 -1.6294 -0.5557 0.7676 0.0821 0.3552 0.2239 -1.4749 -0.2152 1.4882 -1.8534 0.7247 0.3840 -0.5070 0.5453 0.4545 -0.0928 1.1387 0.5270 -0.8375 0.3895 -0.8847 0.0965 -0.1061 -0.5309 -0.8168 -0.5818 -0.1972 -0.5918 0.3532 -0.4726 0.4600 0.8919 0.1430 1.9744 -0.1517 -1.4150 1.1786 0.0183 -1.3742 -0.2159 -0.2090 -0.7888 0.9750 1.5844 0.0273 -0.2821 1.3222 -0.4184 0.0763 0.3400 0.1533 2.5562 1.4607 -0.1399 -0.4604 0.6893 0.2005 -1.3170 -0.2098 -0.2326 0.6855 1.6805 0.3703 0.7937 -0.7302 0.1306 -0.4120 0.5236 -0.7224 0.5459 -1.0916 1.0271 -1.3951 Std Error Residual 0.910 0.931 0.937 0.908 0.930 0.941 0.948 0.772 0.944 0.930 0.874 0.939 0.887 0.936 0.936 0.906 0.934 0.942 0.947 0.862 0.900 0.928 0.935 0.892 0.943 0.898 0.935 0.939 0.944 0.944 0.924 0.927 0.921 0.927 0.944 0.937 0.944 0.937 0.929 0.918 0.943 0.946 0.902 0.944 0.948 0.860 0.786 0.884 0.908 0.946 0.934 0.894 0.877 0.868 0.942 0.942 0.934 0.924 0.937 0.941 0.930 0.880 0.907 0.938 0.917 0.869 0.937 0.936 0.910 0.938 0.944 0.941 0.948 0.888 James P. Geaghan - Copyright 2011 Statistical Techniques II Large example and Variable selection Obs 75 76 77 78 79 80 81 82 83 84 85 86 87 88 89 90 91 92 93 94 95 96 97 98 99 100 101 102 103 104 105 106 107 108 109 110 111 112 113 Obs 1 2 3 4 5 6 7 8 9 10 11 12 13 14 15 16 17 18 19 20 21 22 23 24 25 26 27 28 29 30 31 32 33 34 Appendix 8 Dep Var Predicted Std Error InfRisk Value Mean Predict 3.4000 3.7978 0.3644 4.5000 3.3530 0.1970 2.9000 3.7601 0.1645 4.9000 4.6400 0.3034 4.4000 4.2309 0.1372 5.1000 5.1301 0.2551 2.9000 3.6909 0.4178 3.5000 3.6466 0.2147 5.5000 3.4759 0.1938 4.7000 2.9373 0.2322 1.7000 3.4202 0.2271 4.1000 4.3757 0.1499 2.9000 4.0162 0.3516 4.3000 4.7994 0.2635 4.8000 4.6353 0.1427 5.8000 5.1161 0.2283 2.9000 3.5738 0.1698 2.0000 3.3353 0.1641 1.3000 2.8328 0.3000 5.3000 3.5739 0.1575 5.3000 4.1800 0.2006 2.5000 4.7218 0.2338 3.8000 3.6521 0.1357 4.8000 4.6121 0.2273 2.3000 3.1092 0.1950 6.2000 4.6116 0.2199 2.6000 3.5498 0.1930 4.3000 4.3379 0.2770 2.7000 3.5443 0.2496 6.6000 6.2094 0.4199 4.5000 3.9279 0.1929 2.9000 3.3188 0.3339 1.4000 2.4051 0.2470 2.1000 2.6359 0.2276 5.7000 5.4603 0.3348 5.8000 4.9282 0.3457 4.4000 4.0867 0.3228 5.9000 6.8509 0.6281 3.1000 4.3416 0.2219 Student Residual 0.659 -1.750 -0.593 0.845 0.0883 0.377 0.236 -1.910 -0.228 1.600 -2.121 0.771 0.433 -0.542 0.582 0.502 -0.0993 1.208 0.556 -0.972 0.433 -0.953 0.103 -0.119 -0.563 -0.910 -0.622 -0.210 -0.627 0.374 -0.512 0.496 0.968 0.154 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | -2-1 0 1 2 |* ***| *| |* | | | ***| | |*** ****| |* | *| |* |* | |** |* *| | *| | | *| *| *| | *| | *| | |* | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 95% CL Mean 3.0752 4.5204 2.9624 3.7436 3.4338 4.0863 4.0384 5.2416 3.9589 4.5029 4.6243 5.6359 2.8623 4.5195 3.2208 4.0724 3.0917 3.8602 2.4769 3.3978 2.9699 3.8706 4.0785 4.6730 3.3189 4.7135 4.2769 5.3219 4.3524 4.9182 4.6634 5.5688 3.2371 3.9105 3.0100 3.6607 2.2379 3.4276 3.2616 3.8862 3.7821 4.5779 4.2581 5.1855 3.3830 3.9212 4.1613 5.0629 2.7224 3.4960 4.1755 5.0476 3.1670 3.9326 3.7887 4.8872 3.0493 4.0392 5.3767 7.0421 3.5454 4.3104 2.6567 3.9810 1.9153 2.8950 2.1846 3.0872 4.7964 6.1242 4.2428 5.6137 3.4466 4.7268 5.6055 8.0964 3.9016 4.7815 Annotated SAS example Page 192 95% CL Predict 1.7635 5.8321 1.4116 5.2943 1.8306 5.6895 2.6455 6.6346 2.3099 6.1519 3.1623 7.0979 1.6166 5.7653 1.6978 5.5954 1.5359 5.4160 0.9807 4.8939 1.4660 5.3745 2.4510 6.3005 1.9907 6.0417 2.8272 6.7715 2.7127 6.5579 3.1613 7.0709 1.6425 5.5050 1.4060 5.2646 0.8402 4.8253 1.6468 5.5011 2.2371 6.1228 2.7644 6.6792 1.7315 5.5727 2.6578 6.5665 1.1686 5.0498 2.6606 6.5626 1.6100 5.4896 2.3586 6.3173 1.5792 5.5093 4.1334 8.2854 1.9882 5.8677 1.3052 5.3325 0.4414 4.3689 0.6814 4.5904 3.4460 7.4745 2.9068 6.9497 2.0802 6.0932 4.5777 9.1242 2.3897 6.2935 Output Statistics Cook's D RStudent 0.005 0.6575 0.021 -1.7682 0.002 -0.5909 0.009 0.8442 0.000 0.0879 0.001 0.3758 0.000 0.2352 0.220 -1.9351 0.000 -0.2268 0.018 1.6124 0.102 -2.1576 0.003 0.7699 0.004 0.4313 0.002 -0.5398 0.002 0.5805 0.003 0.4998 0.000 -0.0988 0.006 1.2110 0.001 0.5546 0.025 -0.9713 0.003 0.4311 0.007 -0.9530 0.000 0.1027 0.000 -0.1184 0.001 -0.5614 0.013 -0.9091 0.002 -0.6205 0.000 -0.2090 0.001 -0.6252 0.001 0.3727 0.002 -0.5098 0.002 0.4946 0.009 0.9678 0.000 0.1536 Residual -0.3978 1.1470 -0.8601 0.2600 0.1691 -0.0301 -0.7909 -0.1466 2.0241 1.7627 -1.7202 -0.2757 -1.1162 -0.4994 0.1647 0.6839 -0.6738 -1.3353 -1.5328 1.7261 1.1200 -2.2218 0.1479 0.1879 -0.8092 1.5884 -0.9498 -0.0379 -0.8443 0.3906 0.5721 -0.4188 -1.0051 -0.5359 0.2397 0.8718 0.3133 -0.9509 -1.2416 Hat Diag H 0.0995 0.0577 0.0443 0.1036 0.0595 0.0365 0.0234 0.3516 0.0304 0.0595 0.1694 0.0404 0.1446 0.0471 0.0465 0.1074 0.0505 0.0342 0.0244 0.1919 0.1193 0.0638 0.0483 0.1353 0.0339 0.1237 0.0496 0.0404 0.0316 0.0314 0.0721 0.0663 0.0769 0.0655 Std Error Residual 0.887 0.939 0.945 0.910 0.949 0.924 0.863 0.935 0.939 0.930 0.932 0.947 0.892 0.922 0.948 0.931 0.944 0.945 0.911 0.946 0.938 0.930 0.949 0.932 0.939 0.933 0.939 0.918 0.926 0.862 0.939 0.899 0.927 0.932 0.899 0.895 0.903 0.725 0.933 Cov Ratio 1.1666 0.8845 1.1072 1.1436 1.1590 1.1183 1.1116 1.2200 1.1200 0.9267 0.8823 1.0795 1.2548 1.1161 1.1109 1.1957 1.1479 0.9946 1.0886 1.2436 1.2187 1.0767 1.1452 1.2600 1.0985 1.1584 1.1099 1.1324 1.0887 1.1127 1.1493 1.1436 1.0893 1.1649 DFFITS 0.2185 -0.4375 -0.1272 0.2870 0.0221 0.0732 0.0364 -1.4251 -0.0401 0.4055 -0.9745 0.1579 0.1774 -0.1200 0.1282 0.1734 -0.0228 0.2280 0.0878 -0.4733 0.1587 -0.2488 0.0231 -0.0468 -0.1052 -0.3415 -0.1417 -0.0429 -0.1129 0.0671 -0.1421 0.1318 0.2793 0.0406 James P. Geaghan - Copyright 2011 Statistical Techniques II Large example and Variable selection Student Obs Residual 35 2.092 36 -0.162 37 -1.499 38 1.258 39 0.0197 40 -1.497 41 -0.229 42 -0.221 43 -0.874 44 1.032 45 1.671 46 0.0317 47 -0.359 48 1.496 49 -0.461 50 0.0807 51 0.364 52 0.171 53 2.914 54 1.684 55 -0.149 56 -0.489 57 0.738 58 0.217 59 -1.406 60 -0.223 61 -0.250 62 0.779 63 1.852 64 0.395 65 0.866 66 -0.840 67 0.139 68 -0.440 69 0.576 70 -0.770 71 0.578 72 -1.160 73 1.083 74 -1.570 75 -0.448 76 1.222 77 -0.910 78 0.286 79 0.178 80 -0.0326 81 -0.916 82 -0.157 83 2.155 84 1.894 85 -1.846 86 -0.291 87 -1.251 88 -0.542 89 0.174 90 0.734 91 -0.714 92 -1.413 93 -1.683 94 1.825 95 1.194 96 -2.389 97 0.156 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | -2-1 0 1 2 |**** | **| |** | **| | | *| |** |*** | | |** | | | | |***** |*** | | |* | **| | | |* |*** | |* *| | | |* *| |* **| |** ***| | |** *| | | | *| | |**** |*** ***| | **| *| | |* *| **| ***| |*** |** ****| | Appendix 8 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | Cook's D 0.016 0.000 0.008 0.008 0.000 0.023 0.000 0.000 0.011 0.004 0.007 0.000 0.007 0.044 0.003 0.000 0.001 0.000 0.185 0.070 0.000 0.001 0.003 0.000 0.011 0.000 0.000 0.013 0.045 0.001 0.008 0.017 0.000 0.001 0.004 0.003 0.001 0.006 0.003 0.045 0.004 0.007 0.003 0.001 0.000 0.000 0.022 0.000 0.022 0.025 0.023 0.000 0.027 0.003 0.000 0.004 0.002 0.007 0.034 0.010 0.007 0.040 0.000 RStudent 2.1277 -0.1611 -1.5084 1.2615 0.0196 -1.5064 -0.2280 -0.2199 -0.8731 1.0326 1.6853 0.0316 -0.3573 1.5047 -0.4590 0.0803 0.3623 0.1706 3.0267 1.6988 -0.1478 -0.4872 0.7366 0.2159 -1.4128 -0.2220 -0.2489 0.7773 1.8744 0.3931 0.8649 -0.8387 0.1387 -0.4386 0.5737 -0.7684 0.5766 -1.1615 1.0841 -1.5818 -0.4468 1.2251 -0.9096 0.2845 0.1773 -0.0324 -0.9156 -0.1561 2.1943 1.9187 -1.8684 -0.2898 -1.2545 -0.5397 0.1728 0.7326 -0.7122 -1.4202 -1.6980 1.8457 1.1969 -2.4455 0.1551 Annotated SAS example Page 193 Hat Diag H 0.0318 0.0449 0.0314 0.0454 0.0608 0.0841 0.0332 0.0270 0.1145 0.0300 0.0219 0.1957 0.3277 0.1501 0.1033 0.0265 0.0508 0.1302 0.1635 0.1815 0.0353 0.0361 0.0521 0.0708 0.0460 0.0377 0.0588 0.1573 0.1048 0.0430 0.0865 0.1781 0.0459 0.0479 0.0999 0.0427 0.0316 0.0363 0.0223 0.1419 0.1444 0.0422 0.0294 0.1001 0.0205 0.0707 0.1899 0.0501 0.0408 0.0586 0.0561 0.0244 0.1345 0.0755 0.0221 0.0567 0.0314 0.0293 0.0978 0.0270 0.0438 0.0595 0.0200 Cov Ratio 0.7651 1.1395 0.9251 0.9955 1.1615 0.9789 1.1232 1.1164 1.1528 1.0251 0.8731 1.3561 1.6046 1.0554 1.1943 1.1199 1.1361 1.2509 0.6057 1.0393 1.1286 1.1085 1.0976 1.1692 0.9620 1.1287 1.1527 1.2281 0.9011 1.1245 1.1188 1.2484 1.1414 1.1267 1.1777 1.0823 1.0942 1.0069 1.0074 1.0243 1.2529 0.9999 1.0458 1.2036 1.1106 1.1738 1.2517 1.1460 0.7539 0.8448 0.8562 1.1100 1.0995 1.1503 1.1126 1.1035 1.0775 0.9438 0.9432 0.8365 1.0074 0.6979 1.1108 DFFITS 0.3859 -0.0349 -0.2714 0.2752 0.0050 -0.4564 -0.0423 -0.0366 -0.3140 0.1817 0.2521 0.0156 -0.2495 0.6323 -0.1558 0.0132 0.0838 0.0660 1.3383 0.8000 -0.0283 -0.0942 0.1726 0.0596 -0.3102 -0.0439 -0.0622 0.3358 0.6414 0.0833 0.2661 -0.3904 0.0304 -0.0984 0.1912 -0.1622 0.1041 -0.2255 0.1636 -0.6433 -0.1835 0.2571 -0.1584 0.0949 0.0256 -0.0089 -0.4432 -0.0359 0.4527 0.4788 -0.4555 -0.0459 -0.4945 -0.1542 0.0260 0.1796 -0.1281 -0.2466 -0.5592 0.3073 0.2561 -0.6149 0.0222 James P. Geaghan - Copyright 2011 Statistical Techniques II Large example and Variable selection Student Obs Residual 98 0.202 99 -0.862 100 1.702 101 -1.011 102 -0.0413 103 -0.912 104 0.453 105 0.609 106 -0.466 107 -1.085 108 -0.575 109 0.267 110 0.975 111 0.347 112 -1.312 113 -1.331 Obs 1 2 3 4 5 6 7 8 9 10 11 12 13 14 15 16 17 18 19 20 21 22 23 24 25 26 27 28 29 30 31 32 33 34 35 36 37 38 39 40 41 42 43 44 45 46 47 48 49 50 51 52 53 54 | | | | | | | | | | | | | | | | -2-1 0 1 2 | *| |*** **| | *| | |* | **| *| | |* | **| **| Appendix 8 | | | | | | | | | | | | | | | | Cook's D 0.000 0.004 0.018 0.005 0.000 0.007 0.005 0.002 0.003 0.009 0.002 0.001 0.016 0.002 0.144 0.011 RStudent 0.2007 -0.8607 1.7176 -1.0113 -0.0411 -0.9111 0.4514 0.6072 -0.4642 -1.0857 -0.5734 0.2656 0.9744 0.3455 -1.3169 -1.3358 Annotated SAS example Page 194 Hat Diag H 0.0562 0.0414 0.0526 0.0405 0.0834 0.0677 0.1917 0.0405 0.1212 0.0664 0.0563 0.1219 0.1299 0.1133 0.4289 0.0535 Cov Ratio 1.1517 1.0668 0.8930 1.0402 1.1899 1.0886 1.3258 1.1009 1.2182 1.0546 1.1233 1.2346 1.1544 1.2175 1.6437 0.9875 DFFITS 0.0490 -0.1788 0.4046 -0.2078 -0.0124 -0.2456 0.2198 0.1247 -0.1724 -0.2894 -0.1401 0.0989 0.3765 0.1235 -1.1413 -0.3177 Output Statistics -----------------------------------------DFBETAS----------------------------------------Intercept LtofStay Age CulRatio XRay NoBeds Census Nurses Services -0.0058 -0.0612 0.0559 0.0266 -0.1222 -0.0569 0.0265 0.0288 0.1141 0.0761 -0.0766 -0.1232 0.0709 0.2390 0.0296 0.0403 -0.0008 -0.1732 0.0069 0.0335 -0.0493 0.0042 -0.0077 0.0030 -0.0216 0.0072 0.0805 -0.0561 0.0045 0.0018 -0.0587 0.1880 0.1264 -0.1664 0.0799 -0.0095 -0.0091 0.0040 0.0085 0.0160 -0.0056 0.0005 -0.0026 0.0027 -0.0013 0.0125 -0.0207 -0.0104 0.0155 0.0235 -0.0449 0.0472 -0.0174 0.0131 -0.0188 -0.0080 0.0253 0.0121 -0.0046 -0.0111 0.0114 -0.0032 0.0024 -0.1053 -0.1015 0.1415 -0.9392 0.3270 -0.8654 0.6518 0.2810 0.2112 -0.0192 0.0116 0.0167 -0.0147 -0.0081 -0.0012 -0.0016 0.0103 -0.0031 -0.1378 -0.1386 0.1959 0.3054 -0.0665 -0.0708 0.0629 -0.0804 0.1133 0.2254 0.1898 -0.1289 -0.0027 -0.4323 0.0365 0.0364 -0.4860 0.0604 -0.0475 -0.0578 0.0625 -0.0322 0.0529 0.0372 -0.0108 -0.0781 0.0360 -0.0830 0.0291 0.0532 0.0905 0.0106 -0.0190 -0.0206 0.0836 0.0066 0.0421 0.0780 -0.0694 -0.0554 -0.0266 0.0145 -0.0170 0.0162 -0.0171 -0.0060 -0.0157 0.0436 0.0264 -0.0069 -0.0095 0.0233 -0.0018 -0.0881 0.0378 0.0664 -0.0433 -0.0126 -0.0781 -0.0614 0.0042 0.1298 0.0062 -0.0075 0.0102 0.0062 -0.0075 -0.0097 0.0047 -0.0061 0.0063 -0.0029 -0.0471 0.1035 -0.0023 0.0563 0.0216 -0.0255 -0.0039 0.0125 -0.0043 0.0245 0.0215 -0.0224 -0.0516 -0.0028 -0.0176 -0.0060 0.0371 0.0050 0.0534 0.0356 -0.0380 0.0173 -0.0388 -0.3537 0.2797 0.0235 0.0248 0.1068 -0.0193 -0.0934 0.0078 0.0497 0.0380 -0.0213 -0.0101 -0.0770 -0.0303 0.0401 0.0368 -0.1306 -0.0895 0.0489 -0.0489 -0.0171 0.0556 -0.0009 -0.0082 -0.0002 -0.0003 0.0076 -0.0145 0.0140 -0.0044 0.0141 0.0217 0.0127 -0.0285 0.0007 -0.0055 0.0043 -0.0040 -0.0216 0.0151 -0.0112 0.0245 0.0006 -0.0190 0.0341 0.0542 -0.0409 -0.0057 -0.0653 -0.0449 0.1400 0.0381 0.1104 -0.2315 -0.0002 -0.0141 -0.0985 0.0727 -0.0549 0.0042 0.0594 -0.0453 -0.0351 0.0059 0.0129 -0.0441 0.0269 -0.0161 0.0162 0.0010 -0.0062 0.0164 0.0189 -0.0255 0.0175 -0.0044 0.0164 -0.0407 -0.0045 0.0091 -0.0246 0.0312 -0.0253 -0.0300 0.0483 0.0141 0.0122 -0.0276 -0.0165 0.0394 0.0193 -0.0206 -0.0035 -0.0058 -0.0155 -0.0331 0.0450 0.0382 -0.0336 0.0589 -0.0118 -0.0946 -0.0276 0.0032 0.0012 0.0005 0.0074 -0.0390 -0.0962 0.0559 0.0561 0.0612 0.0281 0.1903 -0.0286 0.0210 -0.1998 -0.0125 -0.0381 0.0993 -0.0653 -0.0115 0.0199 -0.0042 -0.0014 0.0110 0.0012 -0.0001 -0.0122 0.0118 -0.0467 0.0587 0.0057 -0.0964 -0.0679 -0.0897 -0.0014 0.0342 0.2901 0.0167 0.0027 -0.0093 -0.0038 -0.0152 -0.0102 0.0083 0.0131 -0.0171 0.1246 -0.0244 -0.1473 -0.0797 0.0713 0.0215 -0.0171 0.0615 -0.0299 0.1382 -0.0589 -0.1253 -0.1272 0.1091 -0.0757 0.0589 -0.0235 0.0552 0.0004 0.0019 -0.0012 -0.0023 -0.0014 -0.0016 0.0004 0.0005 0.0032 0.0886 0.0540 -0.2360 0.0265 0.0833 -0.0289 -0.0192 0.0048 0.2557 -0.0138 0.0195 0.0069 0.0092 -0.0231 0.0178 -0.0214 0.0037 0.0072 0.0052 -0.0142 -0.0005 -0.0080 -0.0024 0.0037 0.0039 -0.0105 0.0054 -0.1827 -0.2113 0.2495 0.1618 0.0297 -0.0613 0.0909 0.0005 -0.0031 0.0376 -0.0317 -0.0249 -0.0133 -0.0102 -0.1203 0.1211 0.0004 0.0513 0.1139 -0.0952 -0.0655 -0.0032 0.0632 -0.1020 0.0990 -0.0199 0.0005 -0.0000 0.0032 0.0002 -0.0030 -0.0045 0.0072 -0.0080 0.0071 -0.0027 0.0775 -0.2186 0.0207 0.0722 0.0080 -0.0257 0.0549 -0.0182 -0.0122 -0.0879 -0.0938 0.1457 0.0508 -0.0089 0.2387 0.0424 -0.4695 -0.0988 -0.0758 0.0048 0.0186 0.0097 0.0676 0.0099 -0.0307 0.0083 0.0943 0.0030 -0.0051 -0.0026 -0.0051 0.0056 -0.0026 0.0038 -0.0033 0.0051 -0.0375 0.0325 0.0270 0.0075 -0.0226 -0.0246 -0.0032 0.0478 0.0183 0.0091 0.0136 -0.0082 -0.0032 -0.0345 0.0358 -0.0373 0.0083 0.0114 -0.6207 0.2045 0.4722 -0.0177 0.2607 1.0981 -0.8620 -0.2284 -0.3190 0.2203 0.1940 -0.2962 0.4956 -0.0829 0.1343 -0.0902 -0.1464 -0.1429 James P. Geaghan - Copyright 2011 Statistical Techniques II Large example and Variable selection Appendix 8 Annotated SAS example Page 195 -----------------------------------------DFBETAS----------------------------------------Obs Intercept LtofStay Age CulRatio XRay NoBeds Census Nurses Services 55 -0.0062 -0.0084 0.0017 0.0031 0.0174 -0.0049 0.0084 -0.0010 -0.0009 56 0.0240 -0.0544 -0.0066 0.0442 0.0249 -0.0014 0.0198 -0.0184 -0.0328 57 -0.0514 -0.0838 0.0946 -0.0365 0.0393 -0.0069 0.0139 -0.0237 0.0078 58 0.0320 -0.0187 -0.0191 0.0022 -0.0127 -0.0308 0.0209 0.0271 0.0059 59 -0.0487 0.0437 0.0561 0.0392 -0.1383 0.1161 -0.1259 -0.0869 0.0841 60 0.0153 -0.0179 -0.0099 0.0077 -0.0130 -0.0037 0.0049 -0.0082 *0.0218 61 0.0107 -0.0373 -0.0104 0.0096 0.0332 -0.0224 0.0297 -0.0072 0.0075 62 0.0550 -0.0682 -0.0040 0.0715 -0.1211 -0.2090 0.2535 -0.0688 0.0645 63 -0.3925 -0.2981 0.4899 -0.0237 0.2989 -0.0489 0.0799 -0.0238 -0.0754 64 0.0157 0.0206 -0.0239 -0.0450 0.0398 -0.0074 -0.0083 0.0331 -0.0241 65 0.1549 -0.1426 -0.0766 0.0682 -0.0071 -0.0452 0.1068 -0.0342 -0.0722 66 -0.0697 0.0201 -0.0017 -0.0725 0.1108 0.1225 -0.0574 -0.2884 0.1584 67 0.0103 0.0116 -0.0179 -0.0215 0.0102 0.0051 -0.0105 0.0080 0.0055 68 0.0139 0.0563 -0.0236 0.0348 -0.0626 0.0346 -0.0423 0.0045 -0.0112 69 0.0249 -0.0807 0.0007 -0.0311 0.0651 -0.0185 0.0955 -0.1185 -0.0247 70 0.0135 0.0913 -0.0591 -0.1009 -0.0243 0.0068 -0.0308 0.0431 0.0388 71 0.0359 -0.0446 -0.0148 -0.0038 0.0425 0.0011 -0.0039 0.0078 -0.0230 72 -0.0969 0.0703 0.0038 -0.0516 0.1074 0.0058 -0.0101 0.0154 0.0327 73 0.0621 -0.0069 -0.0339 0.0210 -0.0879 -0.0494 0.0580 -0.0351 0.0472 74 0.0967 0.0624 -0.0356 -0.3241 0.1210 0.1577 -0.0777 0.1176 -0.5043 75 -0.1361 -0.0348 0.1609 0.0596 -0.0174 -0.0545 0.0570 0.0279 -0.0424 76 0.1545 -0.1276 -0.0831 -0.0148 0.0619 -0.0504 0.0442 0.0238 -0.0454 77 -0.0854 -0.0215 0.0852 0.0484 -0.0363 0.0078 0.0052 0.0017 0.0168 78 0.0021 -0.0335 0.0085 -0.0098 0.0128 0.0026 0.0291 -0.0316 -0.0075 79 -0.0085 -0.0049 0.0107 0.0011 -0.0027 0.0014 -0.0051 0.0038 0.0108 80 0.0055 0.0010 -0.0053 -0.0053 0.0006 -0.0017 0.0009 0.0037 -0.0027 81 -0.2071 -0.1869 0.2802 0.1750 0.1152 -0.1756 0.1463 0.1520 -0.1607 82 -0.0129 0.0104 0.0138 0.0187 -0.0190 0.0006 -0.0016 0.0081 -0.0125 83 0.1055 -0.0486 -0.0444 0.0137 -0.1684 0.1873 -0.1900 -0.1034 0.1805 84 0.1158 0.1691 -0.0180 -0.0757 -0.2955 0.1548 -0.1765 0.0827 -0.1886 85 0.0695 0.0543 -0.1328 0.0009 0.1940 0.0829 -0.0256 0.0626 -0.2835 86 -0.0090 0.0015 0.0095 -0.0141 0.0073 -0.0132 0.0127 0.0165 -0.0207 87 0.0046 0.2707 -0.0545 -0.0431 -0.0866 -0.0695 -0.0979 0.3829 -0.2057 88 0.0374 -0.0351 0.0029 0.0300 -0.0115 -0.0796 0.0849 0.0365 -0.0977 89 -0.0056 -0.0033 0.0043 0.0013 0.0058 -0.0089 0.0019 0.0080 0.0111 90 0.0514 0.0464 -0.0374 0.0414 -0.0704 -0.0506 0.0443 0.0684 -0.0759 91 -0.0513 -0.0125 0.0451 0.0538 -0.0453 -0.0270 0.0229 0.0025 0.0554 92 0.0022 -0.0436 -0.0423 0.0840 0.0185 -0.0513 0.0589 -0.0273 0.1045 93 -0.1305 -0.0707 0.0437 0.1990 -0.0926 -0.0852 0.0366 -0.0563 0.4469 94 0.0024 -0.0627 0.0760 -0.0029 0.0425 0.0715 -0.0670 0.0353 -0.1565 95 0.1035 0.0670 -0.0960 -0.0556 0.0463 -0.0088 -0.0209 0.1226 -0.1684 96 0.2140 0.2021 -0.2662 -0.3811 0.0772 0.0462 -0.0090 0.1246 -0.3010 97 0.0063 0.0001 -0.0039 -0.0112 -0.0038 0.0008 -0.0033 0.0034 0.0058 98 0.0010 0.0195 -0.0135 -0.0199 0.0142 0.0099 -0.0011 -0.0256 0.0051 99 -0.0738 0.0236 0.0356 0.0422 0.0768 0.0446 -0.0416 0.0409 -0.0754 100 0.0752 -0.0524 -0.0076 0.0739 -0.1939 -0.0467 0.1145 -0.0558 0.0346 101 -0.0512 -0.0964 0.0521 0.1041 -0.0070 -0.0140 0.0429 -0.0635 0.0944 102 -0.0061 -0.0023 0.0089 0.0064 -0.0065 -0.0011 0.0014 0.0013 -0.0018 103 0.0612 0.1326 -0.1215 -0.0262 -0.1112 -0.0508 0.0166 0.0231 0.1012 104 -0.1648 0.0003 0.1142 -0.0262 0.1142 -0.0288 0.0459 -0.0652 0.0682 105 0.0371 0.0358 -0.0184 -0.0213 -0.0699 -0.0147 -0.0130 0.0793 -0.0274 106 0.0663 -0.0789 -0.0728 0.0343 0.0573 -0.0652 0.0726 -0.0264 0.0622 107 -0.1435 0.0716 0.0273 0.0018 0.1223 0.0182 -0.0757 0.1015 0.0813 108 -0.0320 -0.0225 -0.0069 0.0165 0.0787 -0.0410 0.0378 0.0026 0.0473 109 -0.0139 0.0179 -0.0082 -0.0563 0.0552 0.0065 -0.0178 0.0502 -0.0138 110 0.0786 -0.0077 -0.0134 0.3086 -0.1571 0.0268 0.0073 -0.0647 -0.1149 111 -0.0304 -0.0282 0.0330 0.0056 -0.0213 -0.0310 0.0054 0.0020 0.1027 112 0.1180 -0.1095 -0.0938 -0.1728 0.0725 0.3803 -0.6959 0.4691 0.1899 113 0.1581 0.0586 -0.2054 -0.1201 -0.0508 0.0215 -0.0283 0.0088 0.1050 Sum of Residuals Sum of Squared Residuals Predicted Residual SS (PRESS) 0 95.63982 117.92422 James P. Geaghan - Copyright 2011 Statistical Techniques II Large example and Variable selection Appendix 8 Annotated SAS example Page 196 SENIC database from NKNW 1996 (Appendix C) Full Model with diagnostics The REG Procedure Model: MODEL1 Partial Regression Residual Plot -+---------+---------+---------+---------+---------+---------+---------+---------+---------+---------+---------+InfRisk | | | | | | 3 + + | | | 1 | | | | | 2 + 1 1 + | 1 1 1 | | 1 1 1 | | 1 1 | | 1 1 | 1 + 1 1 1 1 + | 12 1 1 | | 1 11 1 31 1 | | 1 1 1 1 121 1 | | 1 1 1 2 1 1 2 1 1 1 1 | 0 + 11 1 1 1 1 1 + | 1 1 1 1 1 1 1 22 1 | | 1 11 1 1 1 | | 1 1 1 1 1 1 1 | | 1 1 1 1 111 | -1 + 1 1 1 1 1 11 + | 1 1 1 | | 1 2 1 1 | | 11 1 1 | | 1 | -2 + + | 1 | | | | | | | -3 + + | | | | -+---------+---------+---------+---------+---------+---------+---------+---------+---------+---------+---------+-0.30 -0.25 -0.20 -0.15 -0.10 -0.05 0.00 0.05 0.10 0.15 0.20 0.25 Intercept ------+----+----+----+----+----+----+----+----+----+----+----+----+----+----+----+----+----+----+----+----+-----InfRisk | | | | | | 3 + + | 1 | | | | | | | 2 + 1 1 1 + | 1 | | 11 | | 1 1 1 1 | | 1 1 1 | 1 + 1 1 1 1 + | 1 1 1 11 1 | | 1 1 1 1 | | 1 1 12 1 2 1 1 111 1 1 | | 1 1 1 1111 1 1 2 1 | 0 + 1 11 1 21 1 1 + | 1 11 1 1 1 | | 2 11 1 1 1 1 3 1 | | 1 1 1 1 | | 1 1 11 1 1 1 | -1 + 1 11 + | 2 11 1 | | 121 1 11 | | 1 1 | | 1 | -2 + 1 + | | | 1 | | | | | -3 + + | | | | ------+----+----+----+----+----+----+----+----+----+----+----+----+----+----+----+----+----+----+----+----+------3.0 -2.5 -2.0 -1.5 -1.0 -0.5 0.0 0.5 1.0 1.5 2.0 2.5 3.0 3.5 4.0 4.5 5.0 5.5 6.0 6.5 7.0 LtofStay -------+------+------+------+------+------+------+------+------+------+------+------+------+------+------+------InfRisk | | | | | | 3 + + | | | 1 | | | | | 2 + 1 1 + | 1 1 1 | | 1 1 1 | | 1 1 | | 1 1 1 | 1 + 1 11 + | 1 1 1 1 1 1 | | 1 2 11 11 1 | | 11 1 1 1 1 1 1 1 | | 1 1 1 1 3 2 1 1 1 | 0 + 1 1 1 11 1 1 + | 1 1 1 1 2 111 111 | | 11 1 1 1 1 1 | | 1 11 1111 1 | | 1 2 1 1 1 | -1 + 11 1 1 1 1 1 1 1 + | 2 | | 1 11 1 | | 1 1 2 | | 1 | -2 + + | 1 | | | | | | | -3 + + | | | | -------+------+------+------+------+------+------+------+------+------+------+------+------+------+------+-------16 -14 -12 -10 -8 -6 -4 -2 0 2 4 6 8 10 12 Age James P. Geaghan - Copyright 2011 Statistical Techniques II Large example and Variable selection Appendix 8 Annotated SAS example Page 197 SENIC database from NKNW 1996 (Appendix C) Full Model with diagnostics The REG Procedure Model: MODEL1 Partial Regression Residual Plot -+---------+---------+---------+---------+---------+---------+---------+---------+---------+---------+---------+3 + + | | | | | 1 1 | | | | 1 | | 1 | 2 + 1 + | 1 | | 1 1 | InfRisk | 1 1 1 | | 1 | | 1 | | 1 1 1 1 | 1 + 1 1 1 + | 1 1 1 | | 1 11 | | 1 1 1 1 1 | | 1 1 1 21 1 | | 1 1 1 1 | | 1 11 1 111 2 1| 0 + 1 1 1 + | 1 1 1 1 1 1 1 1 | | 1 1 1 1 1 1 | | 1 2 1 1 | | 1 1 1 1 1 1 1 | | 1 111 1 1 1 1 | | 1 1 1 1 1 | -1 + 1 1 1 1 1 + | 1 1 | | 1 | | 1 1 1 | | 2 1 1 | | 1 | | 1 1 | -2 + 1 + -+---------+---------+---------+---------+---------+---------+---------+---------+---------+---------+---------+-20 -15 -10 -5 0 5 10 15 20 25 30 35 CulRatio --------+-----+-----+-----+-----+-----+-----+-----+-----+-----+-----+-----+-----+-----+-----+-----+-----+-------InfRisk | | | | | | 3 + + | 1 | | | | | | | 2 + 1 1 + | 1 1 | | 1 | | 1 1 11 1 1 | | 1 1 1 1 | 1 + 1 + | 1 1 1 1 1 1 | | 1 11 1 111 1 | | 1 1 1 1 1 1 11 | | 1 1 1 11 11 1 13 1 1 1 | 0 + 11 11 1 1 1 1 + | 1 1 1 1 1 1 | | 1 1 11 1 1 1 11 1 | | 1 1 1 1 1 11 1 1 1 | | 11 1 2 | -1 + 11 1 1 1 1 + | 1 1 1 1 | | 1 1 1 1 | | 1 1 | | 1 | -2 + 1 1 + | 1 | | | | | | | -3 + + | | | | --------+-----+-----+-----+-----+-----+-----+-----+-----+-----+-----+-----+-----+-----+-----+-----+-----+--------35 -30 -25 -20 -15 -10 -5 0 5 10 15 20 25 30 35 40 45 XRay -+----+----+----+----+----+----+----+----+----+----+----+----+----+----+----+----+----+----+----+----+----+----+InfRisk | | | | | | 3 + + | | | | | 1 | | | 2 + 1 1 + | 1 1 | | 1 1 11 | | 1 | | 1 1 1 1 1 | 1 + 1 1 + | 1 1 1 1 1 1 | | 1 1 1 11111 1 1 | | 1 1 1 1 1 1 1 1 | | 2 11 31 1 1 1 | 0 + 1 1 2 1 1 1 11 + | 1 1 1 1 1 1 1 1 1 1 | | 1 1 1 11 1 1 1 1 | | 1 1 11 1 1 1 | | 1 2 111 1 1 1 | -1 + 1 1 1 1 + | 1 1 1 | | 1 1 1 1 | | 1 1 1 1 | | 1 | -2 + + | 1 | | | | | | | -3 + + | | | | -+----+----+----+----+----+----+----+----+----+----+----+----+----+----+----+----+----+----+----+----+----+----+-90 -80 -70 -60 -50 -40 -30 -20 -10 0 10 20 30 40 50 60 70 80 90 100 110 120 130 NoBeds James P. Geaghan - Copyright 2011 Statistical Techniques II Large example and Variable selection Appendix 8 Annotated SAS example Page 198 SENIC database from NKNW 1996 (Appendix C) Full Model with diagnostics The REG Procedure Model: MODEL1 Partial Regression Residual Plot --------+----+----+----+----+----+----+----+----+----+----+----+----+----+----+----+----+----+----+----+--------InfRisk | | | | | | 3 + + | | | 1 | | | | | 2 + 1 1 + | 1 1 | | 1 11 | | 1 11 | | 1 1 11 | 1 + 1 1 + | 1 1 1 1 1 1 | | 1 2 1 2 1 1 | | 1 2 1 1 11 1 1 1 | | 1 11 11 11 1 1 2 1 | 0 + 1 12 11 1 1 + | 1 111 11 2 1 1 | | 1 11 1 1 1 1 | | 1 1 11 111 1 | | 1 1 1 11 1 1 2 1 1 | -1 + 1 1 1 + | 1 1 1 | | 1 2 1 | | 1 2 | | 1 1 | -2 + + | 1 | | | | | | | -3 + + | | | | --------+----+----+----+----+----+----+----+----+----+----+----+----+----+----+----+----+----+----+----+---------80 -70 -60 -50 -40 -30 -20 -10 0 10 20 30 40 50 60 70 80 90 100 110 Census -----+-----+-----+-----+-----+-----+-----+-----+-----+-----+-----+-----+-----+-----+-----+-----+-----+-----+----InfRisk | | | | | | 3 + + | | | | | 1 | | | 2 + 1 1 + | 1 1 | | 1 2 | | 1 1 | | 1 11 1 | 1 + 1 1 1 1 + | 1 1 2 1 1 | | 1 1 1 1 1 1 1 1 1 | | 1 1 1 1 1 1 11 1 | | 1 1 1 111 2 1 1 | 0 + 1 1 2 1 1 1 + | 1 2 1 11 1 1 1111 1 | | 2 11 1 1 1 | | 1 1 12 1 1 1 | | 11 2 2 1 1 1 | -1 + 1 1 + | 1 11 1 | | 1 1 1 1 1 1 | | 1 1 1 | | 1 | -2 + + | 1 | | | | | | | -3 + + | | | | -----+-----+-----+-----+-----+-----+-----+-----+-----+-----+-----+-----+-----+-----+-----+-----+-----+-----+-----160 -140 -120 -100 -80 -60 -40 -20 0 20 40 60 80 100 120 140 160 180 Nurses -+---------+---------+---------+---------+---------+---------+---------+---------+---------+---------+---------+3 + + | | | | | | | 1 | | | | 1 1 | 2 + + | | | | InfRisk | 1 1 1 1 1 1 | | | | 1 1 1 | | 1 1 1 | 1 + 1 + | 1 1 1 1 1 | | 1 1 1 1 1 1 | | 1 1 1 1 | | 11 11 1 1 | | 1 1 1 1 1 2 12 1 1 1 | | 1 1 2 1 1 | 0 + 1 1 1 1 1 + | 1 11 1 1 | | 1 12 1 1 1 1 | | 1 11 1 1 | | 1 1 | | 1 1 11 1 1 1 | | 1 1 11 1 | -1 + 1 1 1 1 1 + | 1 1 1 1 | | | | 2 1 1 1 1 | | 1 1 | | | | 1 1 | -2 + 1 + -+---------+---------+---------+---------+---------+---------+---------+---------+---------+---------+---------+-25 -20 -15 -10 -5 0 5 10 15 20 25 30 Services James P. Geaghan - Copyright 2011 Statistical Techniques II Large example and Variable selection Appendix 8 Annotated SAS example Page 199 SENIC database from NKNW 1996 (Appendix C) Full Model with diagnostics The REG Procedure Model: MODEL1 Dependent Variable: InfRisk R e s i d u a l ----------+-------+-------+-------+-------+-------+-------+-------+-------+-------+-------+-------+---------RESIDUAL | | | | 3 + + | | | | | 1 | | | | | | | 2 + 1 1 + | | | 1 1 1 | | 1 1 | | 1 1 | | 1 | | 11 1 1 | 1 + 1 1 + | 1 1 1 | | 1 1 1 1 1 | | 1 21 11 | | 1 1 1 1 1 1 | | 1 1 11 1 1 1 | | 1 3 2 2 1 1 1 | 0 + 1 1 1 1 + | 1 1 1 1 1 11 1 | | 1 1 1 1 1 | | 1 1 1 1 1 1 1 | | 1 1 1 1 11 | | 1 1 1 | | 1 1 111 1 1 1 | -1 + 1 1 1 + | 1 1 | | 1 1 1 | | 1 1 1 1 | | 1 1 | | 1 | | 1 | -2 + + | | | 1 | | | | | | | | | -3 + + | | ----------+-------+-------+-------+-------+-------+-------+-------+-------+-------+-------+-------+---------2.0 2.5 3.0 3.5 4.0 4.5 5.0 5.5 6.0 6.5 7.0 7.5 Predicted Value of InfRisk PRED SENIC database from NKNW 1996 (Appendix C) Full Model with diagnostics R e s i d u a l Plot of e*YHat. Legend: A = 1 obs, B = 2 obs, etc. 3 + | | | A | | 2 + A A | A | A A A A | A A | A | AA A A 1 + A A | A A A A | A A A A A | BA AA A A | A AA A A A A A A | A AA AA A AA A A A 0 +-----------------------------------------------AA---A-----A-----------A----------A----------------------------------------| A A B A A A A B A | A A A A | A A AA A A A A A A | A A AA | A A A B A A A -1 + A A A | A A A | A A A A A | A A | A A | A -2 + | A | | | | -3 + | --+----------+----------+----------+----------+----------+----------+----------+----------+----------+----------+---------2.0 2.5 3.0 3.5 4.0 4.5 5.0 5.5 6.0 6.5 7.0 Predicted Value of InfRisk James P. Geaghan - Copyright 2011 Statistical Techniques II Large example and Variable selection 153 154 155 Appendix 8 Annotated SAS example Page 200 proc univariate data=next1 normal plot; var e; TITLE3 'Full model residual analysis'; run; NOTE: The PROCEDURE UNIVARIATE printed page 30. NOTE: PROCEDURE UNIVARIATE used: real time 0.04 seconds cpu time 0.01 seconds SENIC database from NKNW 1996 (Appendix C) Full Model with diagnostics Full model residual analysis The UNIVARIATE Procedure Variable: e (Residual) N Mean Std Deviation Skewness Uncorrected SS Coeff Variation Moments 113 Sum Weights 0 Sum Observations 0.92408169 Variance 0.19655938 Kurtosis 95.6398199 Corrected SS . Std Error Mean Basic Statistical Measures Location Variability Mean 0.000000 Std Deviation Median 0.018329 Variance Mode . Range Interquartile Range 113 0 0.85392696 -0.0822943 95.6398199 0.08693029 0.92408 0.85393 4.77796 1.13707 Tests for Location: Mu0=0 Test -Statistic-----p Value-----Student's t t 0 Pr > |t| 1.0000 Sign M 0.5 Pr >= |M| 1.0000 Signed Rank S -68.5 Pr >= |S| 0.8454 Test Shapiro-Wilk Kolmogorov-Smirnov Cramer-von Mises Anderson-Darling Tests for Normality --Statistic--W 0.993988 D 0.044211 W-Sq 0.026903 A-Sq 0.198655 -----p Value-----Pr < W 0.9091 Pr > D >0.1500 Pr > W-Sq >0.2500 Pr > A-Sq >0.2500 Quantiles (Definition 5) Quantile Estimate 100% Max 2.556167 99% 2.024051 95% 1.680463 90% 1.178595 75% Q3 0.545301 50% Median 0.018329 25% Q1 -0.591769 10% -1.241553 5% -1.474932 1% -1.853377 0% Min -2.221798 James P. Geaghan - Copyright 2011 Statistical Techniques II Large example and Variable selection Appendix 8 Annotated SAS example Page 201 Extreme Observations ------Lowest---------Highest----Value Obs Value Obs -2.22180 96 1.72608 94 -1.85338 11 1.76267 84 -1.72024 85 1.97442 35 -1.62945 2 2.02405 83 -1.53276 93 2.55617 53 Stem 24 22 20 18 16 14 12 10 8 6 4 2 0 -0 -2 -4 -6 -8 -10 -12 -14 -16 -18 -20 -22 Leaf 6 2 7 836 6989 2 32458 797 0899279 5623557 024614567899 238803455679 5541943 88322110 9864310762210 99327 55864421 291 7424 3720 23 5 # 1 Boxplot 0 1 1 3 4 1 5 3 7 7 12 12 7 8 13 5 8 3 4 4 2 1 | | | | | | | | +-----+ | | *--+--* | | | | +-----+ | | | | | | | | | 2 1 ----+----+----+----+ Multiply Stem.Leaf by 10**-1 157 158 159 161 NOTE: NOTE: 162 NOTE: NOTE: Normal Probability Plot 2.5+ * | ++ | *+ | *+ | **+* | ***+ | *++ | *** | +** | +** | +*** | *** 0.1+ *** | *** | *** | **** | ** | **** | ** | *** | ** | **+ | *++ | ++ -2.3+*+ +----+----+----+----+----+----+----+----+----+----+ -2 -1 0 +1 +2 proc reg data=SENIC; TITLE2 'Stepwise regression - backward selection'; model InfRisk = &DepVarList / selection=backward; Run; 113 observations read. 113 observations used in computations. The PROCEDURE REG printed page 31. PROCEDURE REG used: real time 0.10 seconds cpu time 0.07 seconds James P. Geaghan - Copyright 2011 Statistical Techniques II Large example and Variable selection Appendix 8 Annotated SAS example Page 202 SENIC database from NKNW 1996 (Appendix C) Stepwise regression - backward selection The REG Procedure Model: MODEL1 Dependent Variable: InfRisk Backward Elimination: Step 0 All Variables Entered: R-Square = 0.5251 and C(p) = 9.0000 Source Model Error Corrected Total DF 8 104 112 Analysis of Variance Sum of Mean Squares Square 105.74000 13.21750 95.63982 0.91961 201.37982 Parameter Standard Variable Estimate Error Type II SS Intercept -0.74726 1.20763 0.35211 LtofStay 0.17693 0.06906 6.03648 Age 0.01621 0.02226 0.48809 CulRatio 0.04699 0.01075 17.57678 XRay 0.01204 0.00549 4.42782 NoBeds -0.00145 0.00271 0.26220 Census 0.00072796 0.00347 0.04044 Nurses 0.00191 0.00175 1.08719 Services 0.01628 0.01019 2.34765 Bounds on condition number: 34.702, 674.59 F Value 14.37 F Value 0.38 6.56 0.53 19.11 4.81 0.29 0.04 1.18 2.55 Pr > F <.0001 Pr > F 0.5374 0.0118 0.4679 <.0001 0.0304 0.5945 0.8343 0.2794 0.1131 Backward Elimination: Step 1 Variable Census Removed: R-Square = 0.5249 and C(p) = 7.0440 Source > F Model <.0001 Error Corrected Total Variable Intercept LtofStay Age CulRatio XRay NoBeds Nurses Services Parameter Estimate -0.76082 0.18363 0.01557 0.04665 0.01196 -0.00094901 0.00199 0.01614 DF Analysis of Variance Sum of Squares Mean Square F Value 16.57 7 105.69957 15.09994 105 112 95.68026 201.37982 Pr 0.91124 Standard Error 1.20039 0.06095 0.02195 0.01057 0.00545 0.00130 0.00170 0.01012 Type II SS 0.36606 8.27183 0.45899 17.73508 4.39134 0.48680 1.24827 2.31695 F Value 0.40 9.08 0.50 19.46 4.82 0.53 1.37 2.54 Pr > F 0.5276 0.0032 0.4795 <.0001 0.0303 0.4665 0.2445 0.1138 Bounds on condition number: 7.7057, 162.09 James P. Geaghan - Copyright 2011 Statistical Techniques II Large example and Variable selection Appendix 8 Annotated SAS example Page 203 Backward Elimination: Step 2 Variable Age Removed: R-Square = 0.5226 and C(p) = 5.5431 Source Model Error Corrected Total DF 6 106 112 Analysis of Variance Sum of Mean Squares Square 105.24057 17.54010 96.13925 0.90697 201.37982 Parameter Standard Variable Estimate Error Type II SS Intercept -0.01195 0.57099 0.00039725 LtofStay 0.19699 0.05783 10.52453 CulRatio 0.04448 0.01010 17.59563 XRay 0.01189 0.00543 4.33823 NoBeds -0.00103 0.00129 0.57917 Nurses 0.00200 0.00170 1.26422 Services 0.01637 0.01009 2.38761 Bounds on condition number: 7.6446, 129.79 F Value 0.00 11.60 19.40 4.78 0.64 1.39 2.63 F Value 19.34 Pr > F <.0001 Pr > F 0.9833 0.0009 <.0001 0.0309 0.4260 0.2404 0.1077 Backward Elimination: Step 3 Variable NoBeds Removed: R-Square = 0.5197 and C(p) = 4.1729 Source Model Error Corrected Total DF 5 107 112 Analysis of Variance Sum of Mean Squares Square 104.66141 20.93228 96.71842 0.90391 201.37982 Parameter Standard Variable Estimate Error Type II SS Intercept 0.08173 0.55788 0.01940 LtofStay 0.18315 0.05508 9.99423 CulRatio 0.04567 0.00997 18.96154 XRay 0.01247 0.00538 4.86433 Nurses 0.00093910 0.00105 0.72307 Services 0.01400 0.00963 1.91090 Bounds on condition number: 2.6532, 46.546 F Value 0.02 11.06 20.98 5.38 0.80 2.11 F Value 23.16 Pr > F <.0001 Pr > F 0.8838 0.0012 <.0001 0.0223 0.3731 0.1489 Backward Elimination: Step 4 Variable Nurses Removed: R-Square = 0.5161 and C(p) = 2.9592 Source Model Error Corrected Total Variable Intercept LtofStay CulRatio XRay Services Parameter Estimate -0.06358 0.18841 0.04645 0.01205 0.02047 DF 4 108 112 Analysis of Variance Sum of Mean Squares Square 103.93833 25.98458 97.44149 0.90224 201.37982 Standard Error 0.53321 0.05471 0.00992 0.00535 0.00635 Type II SS 0.01283 10.69867 19.76510 4.57751 9.37912 F Value 0.01 11.86 21.91 5.07 10.40 F Value 28.80 Pr > F <.0001 Pr > F 0.9053 0.0008 <.0001 0.0263 0.0017 Bounds on condition number: 1.3578, 20.506 James P. Geaghan - Copyright 2011 Statistical Techniques II Large example and Variable selection Appendix 8 Annotated SAS example Page 204 All variables left in the model are significant at the 0.1000 level. Summary of Backward Elimination Variable Number Partial Model Step Removed Vars In R-Square R-Square C(p) F Value 1 Census 7 0.0002 0.5249 7.0440 0.04 2 Age 6 0.0023 0.5226 5.5431 0.50 3 NoBeds 5 0.0029 0.5197 4.1729 0.64 4 Nurses 4 0.0036 0.5161 2.9592 0.80 163 164 165 167 NOTE: NOTE: NOTE: NOTE: Pr > F 0.8343 0.4795 0.4260 0.3731 proc reg data=SENIC; TITLE2 'Stepwise regression - stepwise selection'; model InfRisk = &DepVarList / selection=stepwise; Run; 113 observations read. 113 observations used in computations. The PROCEDURE REG printed page 32. PROCEDURE REG used: real time 0.07 seconds cpu time 0.07 seconds SENIC database from NKNW 1996 (Appendix C) Stepwise regression - stepwise selection The REG Procedure Model: MODEL1 Dependent Variable: InfRisk Stepwise Selection: Step 1 Variable CulRatio Entered: R-Square = 0.3127 and C(p) = 41.5161 Source Model Error Corrected Total DF 1 111 112 Analysis of Variance Sum of Mean Squares Square 62.96314 62.96314 138.41668 1.24700 201.37982 Parameter Standard Variable Estimate Error Intercept 3.19790 0.19377 CulRatio 0.07326 0.01031 Bounds on condition number: 1, 1 Type II SS 339.64906 62.96314 F Value 272.37 50.49 F Value 50.49 Pr > F <.0001 Pr > F <.0001 <.0001 Stepwise Selection: Step 2 Variable LtofStay Entered: R-Square = 0.4504 and C(p) = 13.3525 Source Model Error Corrected Total Variable Intercept LtofStay CulRatio Parameter Estimate 0.80549 0.27547 0.05645 DF 2 110 112 Analysis of Variance Sum of Mean Squares Square 90.70199 45.35099 110.67784 1.00616 201.37982 Standard Error 0.48776 0.05246 0.00980 Type II SS 2.74400 27.73885 33.39688 F Value 2.73 27.57 33.19 F Value 45.07 Pr > F <.0001 Pr > F 0.1015 <.0001 <.0001 James P. Geaghan - Copyright 2011 Statistical Techniques II Large example and Variable selection Appendix 8 Annotated SAS example Page 205 Bounds on condition number: 1.1195, 4.4779 Stepwise Selection: Step 3 Variable Services Entered: R-Square = 0.4934 and C(p) = 5.9368 Source Model Error Corrected Total DF 3 109 112 Analysis of Variance Sum of Mean Squares Square 99.36082 33.12027 102.01900 0.93595 201.37982 Parameter Standard Variable Estimate Error Type II SS Intercept 0.49133 0.48164 0.97402 LtofStay 0.22391 0.05337 16.47665 CulRatio 0.05420 0.00948 30.59828 Services 0.01963 0.00645 8.65884 Bounds on condition number: 1.2451, 10.57 F Value 1.04 17.60 32.69 9.25 F Value 35.39 Pr > F <.0001 Pr > F 0.3099 <.0001 <.0001 0.0029 Stepwise Selection: Step 4 Variable XRay Entered: R-Square = 0.5161 and C(p) = 2.9592 Source Model Error Corrected Total DF 4 108 112 Analysis of Variance Sum of Mean Squares Square 103.93833 25.98458 97.44149 0.90224 201.37982 Parameter Standard Variable Estimate Error Type II SS Intercept -0.06358 0.53321 0.01283 LtofStay 0.18841 0.05471 10.69867 CulRatio 0.04645 0.00992 19.76510 XRay 0.01205 0.00535 4.57751 Services 0.02047 0.00635 9.37912 Bounds on condition number: 1.3578, 20.506 F Value 0.01 11.86 21.91 5.07 10.40 F Value 28.80 Pr > F <.0001 Pr > F 0.9053 0.0008 <.0001 0.0263 0.0017 All variables left in the model are significant at the 0.1500 level. No other variable met the 0.1500 significance level for entry into the model. Step 1 2 3 4 Variable Entered CulRatio LtofStay Services XRay Variable Removed Summary of Stepwise Selection Number Partial Model Vars In R-Square R-Square 1 2 3 4 0.3127 0.1377 0.0430 0.0227 0.3127 0.4504 0.4934 0.5161 C(p) 41.5161 13.3525 5.9368 2.9592 F Value Pr > F 50.49 27.57 9.25 5.07 <.0001 <.0001 0.0029 0.0263 James P. Geaghan - Copyright 2011 Statistical Techniques II Large example and Variable selection 169 170 171 173 NOTE: NOTE: NOTE: NOTE: Appendix 8 Annotated SAS example Page 206 proc reg data=SENIC; TITLE2 'Multiple regression - RSquare option'; model InfRisk = &DepVarList/selection=rsquare start=3 stop=6 best=8; Run; 113 observations read. 113 observations used in computations. The PROCEDURE REG printed page 33. PROCEDURE REG used: real time 0.05 seconds cpu time 0.05 seconds SENIC database from NKNW 1996 (Appendix C) Multiple regression - RSquare option The REG Procedure Model: MODEL1 Dependent Variable: InfRisk R-Square Selection Method Number in Model R-Square Variables in Model 3 0.4934 LtofStay CulRatio Services 3 0.4852 LtofStay CulRatio Nurses 3 0.4736 LtofStay CulRatio NoBeds 3 0.4735 LtofStay CulRatio Census 3 0.4696 LtofStay CulRatio XRay 3 0.4630 CulRatio XRay Services 3 0.4619 CulRatio XRay Census 3 0.4538 CulRatio XRay Nurses ----------------------------------------------------------------------------4 0.5161 LtofStay CulRatio XRay Services 4 0.5102 LtofStay CulRatio XRay Nurses 4 0.5000 LtofStay CulRatio XRay Census 4 0.4997 LtofStay CulRatio XRay NoBeds 4 0.4956 LtofStay CulRatio Nurses Services 4 0.4956 LtofStay Age CulRatio Services 4 0.4935 LtofStay CulRatio NoBeds Services 4 0.4934 LtofStay CulRatio Census Services ----------------------------------------------------------------------------5 0.5197 LtofStay CulRatio XRay Nurses Services 5 0.5183 LtofStay Age CulRatio XRay Services 5 0.5166 LtofStay CulRatio XRay Census Services 5 0.5163 LtofStay CulRatio XRay NoBeds Services 5 0.5130 LtofStay Age CulRatio XRay Nurses 5 0.5107 LtofStay CulRatio XRay NoBeds Nurses 5 0.5106 LtofStay CulRatio XRay Census Nurses 5 0.5033 LtofStay Age CulRatio XRay Census ----------------------------------------------------------------------------6 0.5226 LtofStay CulRatio XRay NoBeds Nurses Services 6 0.5225 LtofStay Age CulRatio XRay Nurses Services 6 0.5216 LtofStay CulRatio XRay Census Nurses Services 6 0.5191 LtofStay Age CulRatio XRay Census Services 6 0.5187 LtofStay Age CulRatio XRay NoBeds Services 6 0.5169 LtofStay CulRatio XRay NoBeds Census Services 6 0.5134 LtofStay Age CulRatio XRay NoBeds Nurses 6 0.5132 LtofStay Age CulRatio XRay Census Nurses James P. 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